Ok- played with my wiring for a few more hours this morning and here's what I did...
Disconnected the tail light ground wires from the ground bus bar and direct wired them to the ground wire on the trailer wiring harness (without wiring in the grounds for the side marker/running lights). This takes the 4 side marker/running lights out of the equation. It also takes the bus bar out of the equation.
Checked all connections for tightness (currently taped as i have not wanted to solder until I figure this out). Rechecked tail/brake/turn functions and got the same condition (Rt turn light does not blink when brake and parking lights are on, but does blink when the brake is not engaged).
Next...unplugged both tail light units and switched them (right for left). Since I was not having any issues with the left unit (blinker operated brightly with both parking lights and brake engaged), I figured that I could check that it was not the actual right taillight unit that was defective. Made the switch and the problem remained isolated to right side. So the unit is operating correctly...it must be the trailer or vehicle wiring operating the RT unit.
Before I left, I checked my readings at the vehicle connector and found the voltage on the RT turn signal to be between 10.2-11.0 (approx.) when the turn signal is blinking. However, my reading on the LT turn signal shows voltage in the 6.0 to mid-7 range. I was 95% certain that i was checking the right blades (RT vs. LT), but will have to recheck as this doesn't make sense. It would make sense if I have LT & RT readings reversed. If I have the readings reversed, it would lead me to believe that there is something wrong with the wiring harness that connects to the vehicle connector.
I feel like I am getting closer, but this is really testing my patience. Sorry for the long-winded report, but even if it doesn't help anyone else, it will help me to keep track of what I have done so far.
I'll keep ya'll posted!